Understanding units setup for STL
The STL format does not support units. It just records arbitrary X,Y,Z coordinates of the vertices for each face.  Blender cannot know the units you intend.

blender scenes have their own co-ordinate system.  Unit system and Unit Scale just offer consistent display of properties through the user interface.  The objects themselves remain unchanged, because equally these do not have real dimensions either, much like the STL file they just have an arbitrary X,Y,Z.

To fix the problem with your STL you must enable the Scene Unit checkbox in the STL exporter options as shown.  It is also worth using the Selection Only to avoid exporting unwanted geometry.

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Please note that the STL importer also has similar settings.